An EMD and IMF Energy Entropy Based Optimized Feature Extraction and Classication Scheme for Single Trial EEG Signal

For the purpose of improving the classication accuracy of single trial EEG signal during motor imagery (MI) process, this study proposed a classication method which combined IMF energy entropy and improved EMD scheme. Singular value decomposition (SVD), Gaussian mixture model, EMD and IMF energy entropy were employed for the newly designed scheme. After removing noise and artifacts from acquired EEG signals in EEGLAB, SVD was applied, and the singular values were clustered by Gaussian mixture model. The insignicant characteristics indicated by the small SVD values were then removed, and the signals were reconstructed, feeding to EMD algorithm. Those IMFs mapping to δ (cid:0) θ (cid:0) α and β frequencies were selected as the major features of the EEG signal. The SVM classier with RBF, linear, and polynomial kernel functions and voting mechanism then kicked in for classication. The results were compared with that of the traditional EMD and EEMD through simulation, showing that the proposed scheme can eliminate mode mixing effectively and improve the single trial EEG signal classication accuracy signicantly, suggesting the probability of designing a more ecient EEG control system based on the proposed scheme.


Introduction
The functions and working mechanisms of the human brain have attracted inexhaustible research interests. The U.S., EU, Japan and China started "Brain Plan" one after another, expecting to make breakthroughs in the eld of brain research, thus opening a gate to an exciting future full of opportunities and challenges [1][2][3][4]. Brain computer interface (BCI), as a communication channel established between human brain and external environment, provides researchers a new perspective and a useful tool for the study of neural activity. Among all the BCI designs, event-related potential (ERP) based BCI design has been proved to be an effective strategy, which enables a subject to control external equipment via EEG signal produced in the process of "speculating", "perceiving", or "task implementing" [5]. Nonetheless, the low spatial resolution and signal to noise ratio of EEG signals make them easily contaminated by artifacts (such as EOG, EKG, EMG, and power-line interference), thus limiting the use of BCIs [6].
Improving the classi cation accuracy of EEG signals, especially for the single trial EEG signals, has become a serious challenge in the eld. In view of this, the present study focused attention on the improvement of single trial EEG signal classi cation accuracy.
Feature extraction is of great signi cance for brain wave processing and classi cation. EEG features in time domain, such as pro le, standard deviation, correlation, peak value, etc., can be acquired directly, while in frequency domain, the features can be extracted by signal processing method, such as Fourier transform, power spectrum analysis, modern spectral estimation, coherence analysis, etc. However, most of the feature extraction methods base on an assumption that the acquired signals are linear and stationary, which is not suitable for EEG signal analysis. The critical information contained in EEG signals are most likely non-linear and non-stationary. Short-Time Fourier Transform, Gabor Transform, and Wavelet Transform, as they designed for non-linear stationary signal processing, partially resolved this issue [7]. Huang et al. proposed an adaptive signal processing method, Hilbert-Huang Transform (HHT), which based on Empirical Mode Decomposition (EMD) and Hilbert spectrum analysis, providing a better option for non-linear and non-stationary signal processing [8]. HHT has been applied by many researchers and achieved good results. For instance, Kevriv et al. achieved 92.8% classi cation accuracy via combining EMD, discrete Wavelet Transform, and Wavelet packet processing techniques [9]; Taran et al. obtained 90% classi cation accuracy by analyzing the features of intrinsic mode functions (IMF) [10]; Tang et al. improved EEG classi cation accuracy via conditional EMD based one-dimensional and multidimensional convolution neural network and realized EEG based wheelchair control [11]. Previous studies have found that the α and β rhythms are suppressed in the process of motor imagery, while δ and θ rhythms experiencing time and phase locks, making the EEG signals non-linear and non-stationary [12]. Therefore, the present study used EMD to decompose EEG signal. As for entropy, it is a concept originally came from thermodynamics. Shannon employed it in his information theory and de ned it as a measurement of the uncertainty of the source signal. Information entropy has been widely used in many research elds, such as pathological speech quality estimation, recognition fatigue measurement, dysphagia sound classi cation [13][14][15], and EEG based epilepsy diagnosis. These facts inspired us to combine EMD and information entropy in our research. And concurrently we have to deal with the mode mixing issue born with EMD. Although Ensemble Empirical Mode Decomposition (EEMD) proposes a possible way to solve the mode mixing issue [16], it requires the addition of white noise and the decomposition quality is determined by the number of times of averaging, making it less effective.
Tremendous researches have shown that the causes of mode mixing include intermittent signal, pulse interference and noise [17,18]. Reducing the in uences of these factors will improve SNR and present us with much clearer signal features. Singular Value Decomposition (SVD), as it decomposes the signal matrix and assign each vector a singular value, may help us to extract critical features of the signal according to the singular values [19]. The size and variation of the singular values vary with different signals. Inappropriate selection of them may cause information loss or noise increasing, thus a wise selection of singular values is the key to successful classi cation. Traditionally, singular value curve is employed to ful ll the task, yet this method usually depends on the experience of the operator. K-means clustering, another option for singular value selection, is easily affected by the initial data center, thus lacking robustness [20]. Gaussian Mixture Model (GMM) uses a combination of multiple Gaussian distributions to describe data distribution, adaptively optimizing clustering [21,22], making it a more suitable option for non-linear and non-stationary signal classi cation scheme design. After EMD decomposition, the energy entropies [23,24] of intrinsic mode functions mapping to d, q, a and b frequencies will be used as the feature set. In this work, SVD, GMM, EMD and energy entropy were combined to improve the feature extraction performance. The extracted features were then fed to SVM classi ers, which give us the nal results through their voting [25][26][27][28].
Comparing with that of the traditional EMD and EEMD, our results showed that the proposed scheme could eliminate mode mixing more effectively; energy entropies of the IMFs were suitable features for the classi cation of EEG signals generated in the process of MI; voting was a validate mechanism signi cantly improving classi cation accuracy and robustness. It is worth mentioning that all the methods and results we discussed above were regarding to single trial EEG signal classi cation.

Materials And Methods
All the methods and protocols were carried out in accordance with relevant guidelines and regulations and approved by Guizhou Normal University medical ethic committee. Informed consents were obtained from all subjects.

BCI design
In this work, an Oddball paradigm [29] based BCI was designed, for which a rare event will elicit P300 response, an event-related potential corresponding to target stimulation. Five pictures indicating ve directions (up, down, left, right, and stop) were used as visual stimuli. Each stimulation continued for 125 ms, followed by a 600 ms blank interval. A single trial consists of ve stimuli of different directions in random order, one of which would be the target stimulation, eliciting P300 response. The subject was asked to press down corresponding keys on the numpad to mark the target stimulation (the ve directions were mapping to the numpad; up, down, left, right, and stop for number 8,2,4,6, and 5, respectively). A total of 100 trials were recorded via Neuroscan system. The designed BCI was programed in E-prime. Figure 1. Showed the stimulation sequence and the time windows.
1.2 Data collection 32 healthy people (16 males and 16 females) aged between 19-23, without neurological diseases and disabilities, were recruited as our subjects. The subjects were asked sitting in front of a screen, relaxing themselves, avoiding body movements, reducing eye blinks, and focusing their attention on the center of the screen. The BCI designed by us keep presenting direction pictures to the subjects. Once an intended direction shown on the screen, the subjects pressed down a corresponding key to mark it. The EEG signals were recorded in Neuroscan system. Since P300 response usually occur at the parietal occipital region of the scalp, 10 channels around this area (F3, FZ, F4, C3, CZ, C4, P3, PZ, P4, and OZ) were selected for data collection. The sampling frequency was set at 1000 Hz. The data recording was extended for 1 more minute after the task was done and the subjects relaxed themselves. Five datasets in total were collected for each subject.

Simulation
In order to verify the validation of the improved EMD scheme for mode mixing handling, the current study constructed 3 mixed signals with intermittent noises. Since the frequencies of brain waves fall into the range of 0.5-30 Hz, the simulated signals were set in this range with high frequency intermittent noises.
(1) Set the sampling frequency at 1000Hz. Construct a 1000ms sinusoid signal of amplitude 1uV at 3Hz, denote it as S0.
(3) In order to keep the generality, add 12Hz and 12Hz + 25Hz to S1 to form S2 and S3, respectively.
(4) Construct a matrix with S1, S2, and S3, apply SVD and GMM, eliminate insigni cant features corresponding to small singular values and reconstruct the signals. Use EMD to decompose the reconstructed signals, compare the results with that of the direct application of EMD and EEMD.
The simulation results were as following: (1)The original signal and 3 mixed signals are shown in Figure 2.
(2)through SVD and GMM clustering, the critical feature information in signals were accurately extracted. As shown in Figure 3, the red circles indicate singular values corresponding to signi cant features and blue ones indicate insigni cant features (listed only 20 singular values).
The simulation results suggest that the proposed feature extraction scheme have better performance than the traditional EMD and EEMD for removing mode mixing. Moreover, the spectrum analysis showed that the IMF components demonstrated better physical meaning. These results encouraged us to apply this method to actual EEG data analysis.

Data analysis
The following owchart ( Figure 5.) shows our scheme design, comparing with traditional method.

Preprocessing
Preprocessing is an important step affecting feature extraction and classi cation performance. In this work, ltering and artifacts removal were done in EEGLAB [30].

Feature extraction
The preprocessed signals were divided into 725ms segments (125ms stimulation + 600ms blank interval), feeding to SVD and GMM clustering. After the noise, artifacts, and insigni cant features were ltered out, the EEG signals were reconstructed and decomposed via EMD.
An EEG signal x(t) can be decomposed into n IMF components c 1 (t), c 2 (t), … c n (t) and a residue res. If the residue is small enough to be ignored, then the total energy of the IMF components approximately equals to the energy of the original EEG signal, i.e., E = ∑ n i = 1 E i , where E is the energy of the original signal, E i is the energy of the i-th IMF component. If we de ne P i = E i /E, then P i indicates the ratio of the energy of the i-th IMF component over the total energy. Therefore, we have the following de nition: Where H stands for energy entropy.
After being decomposed by EMD, EEMD, and proposed scheme, the energy entropies of the IMFs mapping to δ, θ, α and β frequencies were extracted as the classi cation features.

Classi cation
SVM with RBF, linear, and polynomial kernel functions were used as the classi er. In this study, we trained 5 classi ers by using the 5 data set, each corresponding to one direction for each subject. An incoming unknown signal will pass through the 5 classi ers, and their votes will determine the category of the unknown EEG signal. Since the classi cation accuracy of each classi er was high enough, it is reasonable to expect their votes will give better performance. By feeding the extracted feature sets to SVM classi er and voting, the classi cation accuracies of P300 and that of a single trial EEG signal were achieved.

The classi cation results of P300 response and single trial EEG signals
The classi cation accuracies of P300 responses by using SVM with EMD, EEMD, and our proposed scheme are shown in Figure 6. It is clear that the classi cation accuracies of P300 response with the proposed scheme (96.6%, 96.7%, and 96.1% with RBF, linear, and polynomial kernel functions, respectively) were higher than that of traditional EMD and EEMD. See Figure 6 for details.
A single trial consists of ve consecutive ashes. The classi cation accuracies of single trial EEG signals with the proposed scheme (85.0%, 85.5%, and 81.8% with RBF, linear, and polynomial kernel functions, respectively) were signi cantly higher than that of traditional EMD and EEMD as well. See Figure 7. for details.

The classi cation results with voting
Through voting of SVM classi ers with any of the three types of kernel functions, the classi cation accuracies of P300 responses and single trial EEG signals were signi cantly improved, demonstrating the superiority and robustness of the voting mechanism. (The classi cation accuracies of P300 responses through voting were 98.5%, 98.7%, and 98.0% for RBF, linear, and polynomial kernel functions, respectively. The improvements comparing with traditional EMD were 3.4%, 2.6%, and 2.0%, respectively; the improvements comparing with EEMD were 1.4%, 1.5%, and 0.3%, respectively. The classi cation accuracies of single trial EEG signals, i.e., the moving directions, were 92.4%, 93.6%, and 90.4% for the three types of kernel functions, respectively. The improvements comparing with EMD were 14.9%, 11.4%, and 8.9%, respectively; the improvements comparing with EEMD were 6.1%, 6.8%, and 1.4%, respectively. See Figure 8 and Figure 9 for details.) To sum up, our results showed that: (1) IMF energy entropy is suitable feature for EEG signal classi cation with SVM classi er; (2) our proposed scheme can remove mode mixing more effectively than traditional EMD and EEMD and the decomposed IMFs were more physically meaningful; (3) the proposed voting mechanism signi cantly improved classi cation accuracy.

Discussion
The application of BCI is mainly limited by the classi cation accuracy, making the improvement of it critical. Therefore, the current study focused attention on improving the performance of single trial EEG signal classi cation scheme. The designed BCI was simple and effective, successfully eliciting P300 response. Through simulation we rst veri ed the validation of the proposed scheme, and proved that IMF energy entropy was a suitable feature for single trial EEG signal classi cation. SVD and GMM were applied to remove the insigni cant features. The vectors corresponding to the small singular values contain less information. If we assume that the noises had far less amplitudes than the signals (most likely, it is true for EEG signal processing), then it is safe to consider these vectors insigni cant and remove them. The reconstructed EEG signals would be "cleaner", thus helping to solve the mode mixing problem caused by high frequency intermittent noises in the process of EMD. Some of the IMFs were strongly correlated to certain frequencies. Since the information of brain wave mainly concentrate in the δ, θ, α, and β bands, we selected the corresponding IMFs, computed their energy entropies, and saved them as the feature sets. The improved classi cation results with SVM con rmed that SVD+GMM+EMD is an effective strategy for feature extraction. Since the classi cation accuracy of each SVM classi er for P300 responses was higher than 95%, it is not surprising that the voting of a bunch of these classi ers will improve the performance. A total of 5 classi ers (one for each direction) were trained in the present study, their votes did improve the classi cation accuracies as expected.
There are still some unsolved issues in the process of data collection. The mental state of the subject cannot be effectively and accurately monitored, thus their concentration level cannot be measured and redressed directly, which reduces the occurrences of P300 responses and applicability of the BCI. Moreover, the heavy computation load of SVD limited its performances for high dimensional data set. The prolonged processing time also limited the e ciency of the BCI. A previous study reported that color heterogeneity may increase the attention level of the subject [31]; and Kouziokas proposed a new SVM kernel function which improved classi cation accuracy [32]. These results brought insights for our feature research. We should incorporate elements that improves subject's attention level into BCI design, further optimize the BCI and algorithm, so as to achieve faster processing speed and higher classi cation accuracy. The stimulation sequence and time windows   The SVD and GMM clustering results of the 3 mixed signals Figure 4 The decomposition results of the3 mixed signals by EMD, EEMD and the proposed scheme  The owchart of data analysis Figure 6 Comparison of P300 response classi cation accuracies by using SVM classi ers with EMD, EEMD, and our proposed scheme  Comparison of the classi cation accuracies of single trial EEG signals by using SVM with EMD, EEMD, and our proposed scheme Comparison of P300 response classi cation accuracies through voting Figure 9